Fernando Torres could be fit for the start of the season after it emerged the thigh injury that ended his involvement in the World Cup final was not as serious as had been feared.

Torres suffered only a small tear to his left thigh after coming on as a late substitute in Spain's 1-0 victory over Holland. He has been told to have three weeks of complete rest and will then undergo a specially tailored rehabilitation programme aimed at getting him fit for Liverpool's opening game against Arsenal on 15 August – if he decides to stay at Anfield in the face of persistent interest from Chelsea.

"The initial assessment was he had a mild adductor tear and the Spanish medical staff didn't consider it to be too serious at the time," the club's head of sports science and medicine, Peter Brukner, said. "He had an MRI scan yesterday which confirmed a small tear. He should be able to resume training within two to three weeks and be able to play again within three to four weeks."

Nonetheless, Liverpool's medical staff will adopt a cautious strategy after a dreadful year for Torres in terms of injuries. Torres had struggled to make the World Cup in the first place, after missing the end of last season with injuries to his right knee. His luckless run has included two knee operations, a hernia problem and recurrent hamstring trouble, and his lack of match sharpness was obvious in South Africa, where he failed to score and lost his place after a series of substandard performances.

The latest diagnosis is, however, about as good as Liverpool could have hoped for considering the way Torres went to ground in the closing moments of Sunday's game. Torres had already been given three weeks off, along with the other Liverpool players involved in the final – Pepe Reina, Dirk Kuyt and Ryan Babel – and was not in the club's plans for the Europa League third-round qualifiers on 29 July and 5 August. The draw for those games takes place in Nyon on Friday.

If the injury proves to be more serious, Torres will target the trip to Manchester City on 23 August or the home game against West Bromwich Albion five days later although, before then, he must decide whether he wants to stay at a club that finished seventh in the Premier League last season and lacks the financial muscle for a major recruitment programme.

Chelsea can offer Champions League football and finance, while Manchester City resurrected their interest after Rafael Benitez's departure from Anfield and are continuing to monitor the striker's potential availability, albeit more in hope than expectation.

The new Liverpool manager, Roy Hodgson, is planning to visit Torres in Spain as he attempts to convince the forward to stay. Liverpool continue to insist he is not for sale.